Police and London Ambulance Service were called at 2.18am on Sunday, 4 April, to a seriously injured woman inside a block of flats in Ravine Grove, SE18.
Officers attended and found a woman suffering stab injuries. Despite the efforts of paramedics, the woman died around an hour later.
A post-mortem examination will be arranged in due course. Officers are working to establish the identity of the woman.
A 39-year-old man was arrested at the scene on suspicion of murder. He remains in custody at a south London police station.
Police cordons remain in place at the location. Enquires continue to establish the full circumstances.
Any witnesses, or anyone with information that may assist police, are asked to call 101 or tweet @MetCC quoting ref 914/04APR